To prove our main result, we rely on the use of cone programming, also called linear conic optimisation. Cone programming is a generalisation of semidefinite programming which is another class of optimisation problems which has seen many uses in quantum theory.
The generalisation of semidefinite programming to cone programming mirrors that of quantum theory to GPTs.
For this reason, cone programming is a natural tool to have handy when studying post-quantum theories.
Although cone programming is a well-studied area of optimisation theory, it has only had a small number of applications in quantum theory [1]}, [2]}, [3]}, [4]}, [5]} and in GPTs [6]}, [7]}, [8]}, [9]}, [10]}.
We hope this work will inspire future applications of cone programming in the study of GPTs and solidify it as an indispensable mathematical tool.
